For this post, I used a statistic called Weighted Runs Created (wRC). I explain it in more detail below, but for now just know that each wRC value is equal to that many runs.
In the graph, the Braves' wRC is broken down by position (and by player within each position). The area of each section is proportional with the wRC at that position. A bigger area = more runs created. The dark outlines represent the MLB averages for each position.
On the season (this does not include yesterday's game), the Braves' offense has been 30 runs worse than the average offense. To make this a fair comparison, it only counts position players, not pitchers or designated hitters. Over 67 games, that's 0.45 fewer runs per game. The Braves have been above average at only 3 positions: catcher, left field, and (barely) third base.
Position-by-position analysis and an explanation of wRC after the jump.
Catcher (+16 wRC compared to an average team)
Brian McCann and David Ross, unsurprisingly, have been worth much more than the average team's catchers: 46 wRC compared to an average of 30 (more than 50% better). That's the best mark in the NL, and 2nd-best in MLB behind the Tigers (whose Victor Martinez has spent a lot of time at DH).
Left Field (+11 wRC)
In left field, Martin Prado and Eric Hinske have done a good job (52 wRC, which is 11 runs above average). Both of them have seen a good deal of time at other positions, though, so you might want to spread a few of those runs around to 3B, RF, and 1B. Clearly, though, left field has been one of the team's few bright spots.
Third Base (+1 wRC)
Chipper Jones has been slightly better than average at third base, putting up 34 wRC, 1 more than the average team's 3B. This does not count the contributions of Prado and others on Chipper's rest days, so the figure should perhaps be even higher.
Shortstop (-4 wRC)
The Braves' shortstops have been nearly equal to the average team's shortstops (28 wRC vs. 32 for an average team), and given Alex Gonzalez's stellar defense, I'm sure most Braves fans will take that.
Center Field (-9 wRC)
First Base (-10 wRC)
At first base, the problem is not so much that Freddie Freeman has been bad (he hasn't) as that the offensive standard is extremely high at that position. Freddie's 32 wRC is 4th-best on the team, but that says more about the team's offensive struggles than about Freeman's successes. Even if you add a few runs for the other players who have filled in at first in Freddie's absence, the Braves are still clearly below-average at this position.
Second Base (-13 wRC)
The Braves' worst production has been at second base, where the bar is much lower than at first base. Still, their 22 runs at that position is 13 runs lower than the average team. If Dan Uggla is really starting to get back into form, we should expect this position to be a strength rather than a weakness for the rest of the season.
Right Field (-19 wRC)
In right field, a combination of injury (to Jason Heyward) and ineffectiveness (of everyone else) has led to a poor production of 26 runs, which is 19 runs below average for that position. Right field has been the best offensive position in MLB so far (average of 45 wRC, edging out 1B), but the Braves have gotten their second-lowest production from that spot.
More About wRC
The statistic wRC summarizes a player's total offensive contributions in one run value. The "weighted" part of the name means that different events count for different fractions of a run, so a double counts for more than a single (not twice as much, though). Each event's value is determined by historical averages for that event, adjusted to today's environment. So a single today counts more than a single 10 years ago, because the average number of runs scored is less today than it was in the go-go early 2000's.
The total number of wRC in the league is scaled to the total number of runs scored, and each team's overall wRC value tends to track very closely with its total runs scored. Thus, you can use wRC to easily portion out the credit for a team's run-scoring, as I did in the graphic. Since the Braves had scored 261 runs (before yesterday's game) and Alex Gonzalez had a 27 wRC, you can give him credit for a bit more than 10% of the Braves' offense.